# Bài 71 trang 40 SGK Toán 9 tập 1

##### Hướng dẫn giải

Sử dụng công thức: $$\begin{array}{l} \sqrt {AB} = \sqrt A .\sqrt B \,\,\left( {A \ge 0,B \ge 0} \right)\\ \sqrt {{A^2}} = \left| A \right| \end{array}$$

$$\sqrt {\frac{A}{B}} = \frac{1}{{\left| B \right|}}\sqrt {AB} ;\,\,\frac{A}{{\sqrt B }} = \frac{{A\sqrt B }}{B}\left( {B > 0} \right)$$

Lời giải chi tiết

a)

\eqalign{ & \left( {\sqrt 8 - 3.\sqrt 2 + \sqrt {10} } \right)\sqrt 2 - \sqrt 5 \cr & = \sqrt {16} - 6 + \sqrt {20} - \sqrt 5 \cr & = 4 - 6 + 2\sqrt 5 - \sqrt 5 = - 2 + \sqrt 5 \cr}

b)

\eqalign{ & 0,2\sqrt {{{\left( { - 10} \right)}^2}.3} + 2\sqrt {{{\left( {\sqrt 3 - \sqrt 5 } \right)}^2}} \cr & = 0,2\left| { - 10} \right|\sqrt 3 + 2\left| {\sqrt 3 - \sqrt 5 } \right| \cr & = 0,2.10.\sqrt 3 + 2\left( {\sqrt 5 - \sqrt 3 } \right) \cr & = 2\sqrt 3 + 2\sqrt 5 - 2\sqrt 3 = 2\sqrt 5 \cr}

Vì $$- 10 < 0;\sqrt 3 < \sqrt 5 \Leftrightarrow \sqrt 3 - \sqrt 5 < 0$$

c)

\eqalign{ & \left( {{1 \over 2}.\sqrt {{1 \over 2}} - {3 \over 2}.\sqrt 2 + {4 \over 5}.\sqrt {200} } \right):{1 \over 8} \cr & = \left( {{1 \over 2}\sqrt {{2 \over {{2^2}}}} - {3 \over 2}\sqrt 2 + {4 \over 5}\sqrt {{{10}^2}.2} } \right):{1 \over 8} \cr & = \left( {{1 \over 4}\sqrt 2 - {3 \over 2}\sqrt 2 + 8\sqrt 2 } \right):{1 \over 8} \cr & = {{27} \over 4}\sqrt 2 .8 = 54\sqrt 2 \cr}

d)

\eqalign{ & 2\sqrt {{{\left( {\sqrt 2 - 3} \right)}^2}} + \sqrt {2.{{\left( { - 3} \right)}^2}} - 5\sqrt {{{\left( { - 1} \right)}^4}} \cr & = 2\left| {\sqrt 2 - 3} \right| + \left| { - 3} \right|\sqrt 2 - 5\left| { - 1} \right| \cr & = 2\left( {3 - \sqrt 2 } \right) + 3\sqrt 2 - 5 \cr & = 6 - 2\sqrt 2 + 3\sqrt 2 - 5 = 1 + \sqrt 2 \cr}